I am asked this for homework:
I am trying to do nodal analysis for part A of the question but am running into problems with number of unknowns versus number equations. Assuming I chose my nodes correctly I get:
$$V_a = V_1 + \frac{V_a}{R_2} + \frac{V_a-V_b}{R_F} + \frac{V_a-V_x}{R_1} $$
$$V_b = V_2 + \frac{V_b-V_x}{R_3} + \frac{V_b-V_a}{R_F} + \frac{V_b}{R_4} $$
I don't believe my node equations are correct but I believe that there is 3 unknowns (Va, Vb, and Vx | V1, V2, all resistors are known(?) ) and only two equations. I tried super position as well treating each stage as an inverting and noninverting with sources on and off.
Any help or guidance on how to approach this problem so that I can reduce it down into the given form would be appreciated .
Note: Vref does not equal ground.
Best Answer
For op-amp problems, assuming negative feedback is present, the inverting and non-inverting inputs (ideally) have the same voltage.
Thus, for example, for the first op-amp, both inputs have a voltage of \$v_1\$. So, how to proceed?
The correct node equation for node A is:
\$\dfrac{v_1 - V_{REF}}{R_2} + \dfrac{v_1 - v_x}{R_1} + \dfrac{v_1 - v_2}{R_F} = 0\$
Can you take it from here?